9.1 Generalized basic model Assume that the relation between consumption and pollution is described by the more general function c = af (x), where f 

(x) > 0 and f 

(x) < 0. The objective function can then be written as U(x) = u(af (x)) − v(x).

1. State the necessary condition for utility maximization. Show also that U

(x) < 0.

2. Characterize the evolution of x over time, that is as a grows.